On Fliess operators driven by L2-Itô random processes

Fliess operators with deterministic inputs have been studied since the late 1970´s and are well understood. When the inputs are stochastic processes the theory is less developed. There have been several interesting approaches for Wiener process inputs. But the interconnection of systems is not well-posed in this context, and this limits their use in applications. This paper has two specific goals. The first goal is to describe the theoretical framework under which a Fliess operator can be driven by a class of L₂-Ito random processes. The second goal is to derive a sufficient condition for the stochastic convergence of the series which defines the corresponding output process.